Unit 8 Magnetism

Magnets Poles of a magnet are the ends where objects are most strongly attracted Like poles repel and unlike poles attract Magnetic poles cannot be isolated

Magnets always have two poles

Types of Magnetic Materials Soft magnetic materials, such as iron, are easily magnetized  They also tend to lose their magnetism easily Hard magnetic materials, such as cobalt and nickel, are difficult to magnetize  They tend to retain their magnetism

Concept Check The north-pole end of a bar magnet is held near a stationary positively charged piece of plastic. Is the plastic...  a) attracted  b) repelled  c) unaffected by the magnet?

More About Magnetism An unmagnetized piece of iron can be magnetized by rubbing it with a magnet  Somewhat like rubbing an object to charge it Magnetism can be induced  If a piece of iron, for example, is placed near a strong permanent magnet, it will become magnetized

Magnetic Fields A magnetic field surrounds a magnetized magnetic material The region of space surrounding a moving charge includes a magnetic field  The charge will still be surrounded by an electric field

Magnetic Field, B A vector quantity Symbolized by “B” Direction is given by the direction a north pole of a compass needle points in that location SI unit: tesla, T  1 T = 1 N/(C m/s)  1 T = 10^4 G (gauss) Out of page Into page

A Few Typical B Values Junk yard magnets  G or 1 Conventional laboratory magnets  G or 2.5 T Superconducting magnets  G or 30 T Earth’s magnetic field  0.5 G or 5 x T

Concept Check In what direction are each of the magnetic fields acting?

Magnetic Field Lines Magnetic field lines are useful for visualizing the magnetic field Magnetic flux (the number of magnetic field lines per unit area) leaves the N pole and enters the S pole and form continuous loops

Rank the magnetic flux in increasing order:

Magnetic Field Lines Iron filings are used to show the pattern of the magnetic field lines

Earth’s Magnetic Field

Source of the Earth’s Magnetic Field There cannot be large masses of permanently magnetized materials since the high temperatures of the core prevent materials from retaining permanent magnetization The most likely source of the Earth’s magnetic field is believed to be electric currents in the liquid part of the core

Magnetic Force When a charged particle is moving through a magnetic field, a magnetic force acts on it  This force has a maximum value when the charge moves perpendicularly to the magnetic field lines  This force is zero when the charge moves along the field lines

Direction of Magnetic Force Experiments show that the direction of the magnetic force is always perpendicular to both v and B

Right Hand Rule Point your fingers in the direction of v Curl the fingers in the direction of the magnetic field, B Your thumb points in the direction of the force F, on a positive charge  If the charge is negative, the force is opposite that determined by the right hand rule

Example What direction is the magnetic force acting on the positive charge?

Example A magnetic field going into the page creates a leftward magnetic force on a positive charge. What direction is the charge moving in? B F

Example An electron feels a force up while it is moving into the paper. Which way is the magnetic field pointing?

Example What direction is the magnetic force on the protons in these problems?

Concept Check

A point charge of +1 μC moves with velocity v into a uniform magnetic field B directed to the right, as shown above. What is the direction of the magnetic force on the charge? a) to the right and up the page b) directly out of the page c) directly into the page d) to the right and into the page e) to the right and out of the page

Magnetic Field/Force B= Magnetic Field (T) F=Magnetic Force (N) q=Charge (C ) v= Velocity (m/s) Θ = Angle between v and B (degrees) F=Bqvsinθ

Example Particle 1, with charge q1=3.6 μC and a speed v1= 862 m/s travels at right angles to a uniform magnetic field. The magnetic force it experiences is 4.25 x 10^-3 N. Particle 2, with a charge q2=53.0 μC and speed v2=1300 m/s moves at an angle of 55 degrees relative to the same magnetic field. Find:  a) The strength of the magnetic field  b) The magnitude of the magnetic force on particle 2

Force on a Wire In this case, there is no current, so there is no force

Force on a Wire B is into the page The current is up the page The force is to the left

Force on a Wire B is into the page The current is down the page The force is to the right

Force on a Wire The magnetic force is exerted on each moving charge in the wire F = B I ℓ sin θ I = Current (A) ℓ = Length of wire (m)  θ is the angle between B and the direction of I  The direction is found by the right hand rule, placing your fingers in the direction of I instead of v

Example A wire carries a current of 22 A from west to east. Assume the magnetic field of Earth at this location is horizontal and directed from south to north and it has a magnitude of 0.05 mT. Find the magnitude and direction of the magnetic force on a 36 m long wire.

Example A wire carries a current of 22 A from west to east. Assume the magnetic field of Earth at this location is horizontal and directed from south to north and it has a magnitude of 0.05 mT. Find the gravitational force is the same 36 m wire is made of copper (density=8.96 g/cm -3 ) and has a cross sectional area of 2.5 x 10 μm 2.

You Do What current would make the magnetic force in the previous examples equal in magnitude to the gravitational force?

Force on a Charged Particle in a Magnetic Field The magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle

Force on a Charged Particle Equating the magnetic and centripetal forces: F=qvBsinθ F=ma

Force on a Charged Particle Solving for r: r=mv/qB -r = radius of orbit (m) -r is proportional to momentum of particle and inversely proportional to magnetic field -Called the cyclotron equation

Example An electron moves in a circular path perpendicular to a uniform magnetic field with a magnitude of 2.0 mT. If the speed of the electron is 1.5 x 10^7 m/s... a) determine the radius of the path. b) determine the time it takes for the electron to complete one revolution.

Mass Spectrometer The mass spectrometer is an instrument which can measure the masses and relative concentrations of atoms and molecules. It makes use of the basic magnetic force on a moving charged particle.

Mass Spectrometer

Example A charged particle enters the magnetic field of a mass spectrometer at a speed of 1.79 x 10^6 m/s. It subsequently moves in a circular orbit with a radius of 16 cm in a uniform magnetic field of 0.35 T having a direction perpendicular to the velocity. Find the particles's mass-to- charge ratio.

Example Use the table to identify what type of particle it is ParticleMass (kg)Charge (C)m/q (kg/C) Hydrogen1.67 x 10^ x 10^ x 10^-8 Deuterium3.35 x 10^ x 10^ x 10^-8 Tritium5.01 x 10^ x 10^ x 10^-8 Helium x 10^ x 10^ x 10^-8

Particle Moving in an External Magnetic Field If the particle’s velocity is not perpendicular to the field, the path followed by the particle is a spiral  The spiral path is called a helix

Recall Constant Velocity 1. What value must be zero in order for a particle to have a constant velocity? (Hint: think back to the definition of displacement, velocity, and acceleration) 2. What are two ways that this value could become zero?

Sample Test Questions: Why doesn't a constant uniform magnetic field do work on a moving charged particle? a) B is conservative field b) F is velocity dependent c) B is vector field, and work is a scalar d) B is scalar field, and work is a vector e) F is always perpendicular to the velocity of particle

Sample Test Questions: A negatively charged particle enters a uniform magnetic field that is perpendicular to the particle's velocity. Which of the following is true of the particle's kinetic energy and direction? a) KE increases, Dir changes b) KE decreases, Dir changes c) KE constant, Dir changes d) KE constant, Dir constant e) KE increases, Dir constant

Sample Test Questions: The region in space surrounding a static electron contains: a) gravitational field b) magnetic field c) electric field d) both an electric field and a magnetic field e) all of the above

Sample Test Questions: Each of the positive ions that pass through crossed electric and magnetic fields without being deflected have the same: a) speed b) mass c) momentum d) energy e) potential

Sample Test Questions:

Hans Christian Oersted 1777 – 1851 Best known for observing that a compass needle deflects when placed near a wire carrying a current  First evidence of a connection between electric and magnetic phenomena

Magnetic Fields – Long Straight Wire A current-carrying wire produces a magnetic field The compass needle deflects in directions tangent to the circle  The compass needle points in the direction of the magnetic field produced by the current

Direction of the Field of a Long Straight Wire Right Hand Rule #2  Grasp the wire in your right hand  Point your thumb in the direction of the current  Your fingers will curl in the direction of the field

Find the direction of the current:

Magnitude of the Field of a Long Straight Wire The magnitude of the field at a distance r from a wire carrying a current of I is: B= µ o = 4π x T. m / A µ o is called the permeability of free space

Example A long, straight wire carries a current of 5 A. A proton at 4 mm from the wire travels at a speed of 1.5 x 10^3 m/s parallel to the wire and in the same direction of the current. a) Find the magnitude and direction of the magnetic field created by the wire. b) Find the magnitude and direction of the magnetic force the wire's magnetic field would exert on the proton.

André-Marie Ampère 1775 – 1836 Credited with the discovery of electromagnetism  Relationship between electric currents and magnetic fields

Magnetic Force Between Two Parallel Conductors The force on wire 1 is due to the current in wire 1 and the magnetic field produced by wire 2 The force per unit length is:

Force Between Two Conductors Parallel conductors carrying currents in the same direction attract each other Parallel conductors carrying currents in the opposite directions repel each other

Magnetic Field of a Current Loop The magnitude of the magnetic field at the center of a circular loop with a radius R and carrying current I is B= μ o I / 2R

Example Given a current carrying circular loop with a diameter of 5 cm and current of 38 A, find the magnetic field at the center of the loop. What would the current have to be if to keep the magnetic field the same but the diameter is doubled?

Magnetic Field of a Solenoid If a long straight wire is bent into a coil of several closely spaced loops, the resulting device is called a solenoid It is also known as an electromagnet since it acts like a magnet only when it carries a current

Applications of Solenoids Locking Applications -Door locks for offices, hotels, and high security area Medical Application -Essential component for dialysis machines. Automotive Solenoid Applications -Interlocking in the gearbox drive selectors, AC controls, entertainment release mechanisms, and security systems. -Some joystick controls designed for games. Industrial Use -In devices that require locking, positioning, pinching, holding, rotating, diverting, valve operation, and more. -Sprinkler systems, air pressure in the air conditioning systems, and irrigation.

Magnetic Field of a Solenoid The field lines inside the solenoid are nearly parallel, uniformly spaced, and close together -This indicates that the field inside the solenoid is nearly uniform and strong The exterior field is nonuniform, much weaker, and in the opposite direction to the field inside the solenoid

Mini Lab: Build a Solenoid 1. Construct a loop of wire with a current. 2. Observe how the magnetic field produced by the loop affects a compass by placing a compass in the middle of the loop. 3. Construct a solenoid with a current. 4. Observe how the magnetic field produced by the solenoid affects a compass by placing a compass in the center of the solenoid. 5. Which do you think has a stronger magnetic field and why?

Magnetic Field in a Solenoid The field lines of a closely spaced solenoid resemble those of a bar magnet

Magnetic Field in a Solenoid The magnitude of the field inside a solenoid is constant at all points far from its ends B = µ o n I -n = N / ℓ -n is the number of turns per unit length The same result can be obtained by applying Ampère’s Law to the solenoid

Example A certain solenoid consists of 100 turns of wire and has a length of 10 cm. a) Find the magnitude of the magnetic field inside the solenoid when it carries a current of 0.5 A. b) What is the momentum of a proton orbiting inside the solenoid in a circle with a radius of 0.02 m? The axis of the solenoid is perpendicular to the plane of the orbit. c) Approximately how much wire would be needed to build this solenoid? Assume the radius is 5 cm.